"Education is the kindling of a flame but not the filling of a vessel."

-Socrates

When by education, the spirit of inquiry is kindled; one acquires a rational mind and can critically think. Likewise, when one acquires knowledge regarding the English language it not only changes the overall game in the exam but also leaves an impression of good writing skills on the examiner. 

What role does English play in CEED/UCEED, NID and NIFT exams? How can I improve in this with a short passage of time? Is it necessary to follow any book related to English proficiency? 

The answer is, hidden between the lines! 

"Practice, Practice and Practice". 

The key to improving at anything is practicing it several times but mindfully. One point to take into consideration is "Maximum efforts with a minimum time limit."

One of the significant steps we can take to achieve this goal is to read comprehension passages as much as possible. Nextly read a little bit of essential grammar that are vividly asked in the NIFT

In my opinion, you should check out the Arihant Publication book for NIFT/NID

Remember, there is always a smarter way to do things! You just need to find your method of doing the task. Until then, keep reading the right stuff! :)